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Radius Formula:
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The formula calculates the radius of a circle when given the chord length and sagitta (the height from the chord to the arc). This is particularly useful in geometry, engineering, and construction applications where circular measurements are involved.
The calculator uses the geometric formula:
Where:
Explanation: This formula derives from the geometric relationship between a chord, its sagitta, and the circle's radius, using the intersecting chords theorem.
Details: This calculation is essential in architecture for designing arches, in engineering for circular structures, in surveying for curved boundaries, and in various manufacturing processes involving circular components.
Tips: Enter chord length and sagitta in consistent units (both meters or both feet). Both values must be positive numbers greater than zero for accurate calculation.
Q1: What is sagitta in circular geometry?
A: Sagitta is the perpendicular distance from the midpoint of a chord to the arc of the circle. It represents the "rise" of the arc above the chord.
Q2: Can this formula be used for any chord position?
A: Yes, the formula works for any chord of a circle, as long as you have the chord length and the corresponding sagitta measurement.
Q3: What are the units for the result?
A: The radius will be in the same units as your input values. If you enter meters, the result will be in meters; if you enter feet, the result will be in feet.
Q4: Are there limitations to this formula?
A: The formula assumes a perfect circular arc and may not be accurate for elliptical or other non-circular curves. It also requires precise measurements of both chord and sagitta.
Q5: How accurate is this calculation?
A: The calculation is mathematically exact for perfect circles. The practical accuracy depends on the precision of your chord and sagitta measurements.